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Number Theory Seminar

Title: Poles of Quotients of $L$-functions and primitivity of $L$-functions of $\mathrm{GL}_3$
Speaker: Ravi Raghunathan (IIT Bombay)
Date: 22 March 2024
Time: 2 pm
Venue: LH-1

Given two distinct cuspidal automorphic $L$-functions (of $\mathrm{GL}_n$ and $\mathrm{GL}_m$ over $\mathbb{Q}$) one expects that their quotients will have infinitely poles, but this is surprisingly hard to prove. In this talk, I will discuss my recent work on the case $m=n-2$ and the primitivity of the $L$-functions of cuspidal automorphic $L$-functions of $\mathrm{GL}_3$. These methods also work for Artin $L$-functions and, more generally, for the $L$-functions of Galois representations under further hypotheses.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 20 Apr 2024